EP3200384A1 - Verfahren zur ausführung einer kryptographischen berechnung und anwendung auf die klassifizierung durch support-vector-maschinen - Google Patents

Verfahren zur ausführung einer kryptographischen berechnung und anwendung auf die klassifizierung durch support-vector-maschinen Download PDF

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EP3200384A1
EP3200384A1 EP17153545.3A EP17153545A EP3200384A1 EP 3200384 A1 EP3200384 A1 EP 3200384A1 EP 17153545 A EP17153545 A EP 17153545A EP 3200384 A1 EP3200384 A1 EP 3200384A1
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data
unit
function
client
result
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French (fr)
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EP3200384B1 (de
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Constance MOREL
Julien Bringer
Hervé Chabanne
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Idemia Identity and Security France SAS
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Safran Identity and Security SAS
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/70—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer
    • G06F21/71—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information
    • G06F21/72—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information in cryptographic circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/46—Secure multiparty computation, e.g. millionaire problem
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/50—Oblivious transfer

Definitions

  • the invention relates to a method for executing a cryptographic calculation implemented jointly between two processing units, in which a function of two variables is evaluated by the two parties, having for inputs data held respectively by each part, without one party learning information about the data held by the other party.
  • the invention applies in particular to the secure classification according to a classifier of a support vector machine whose classifier uses a core of the radial basic function type.
  • a data classification technique is already known according to a classifier of a Support Vector Machine (SVM). This technique consists in classifying an input data x by evaluating a function called classifier H in the data x, and comparing the result of H (x) to a threshold.
  • SVM Support Vector Machine
  • H (x) For example, in the case of a classification in two classes denoted 1 and -1, we compare H (x) with a threshold b and, if H (x) is smaller than b, x is determined as belonging to class 1 and if H (x) is greater than b, x is determined as belonging to the class -1.
  • the definition of the classifier depends of course on the definition of classes. To simplify its calculation, the classifier can be written with a predefined kernel function.
  • a first example of a core function is a Radial Basis Function (RBF), which is a real-valued function whose value depends only on the distance of the data x to a data Y which is a parameter of classifier.
  • RBF Radial Basis Function
  • a kernel-based kernel function can be a Gaussian kernel of the form ⁇ e - ⁇ ⁇ x - Y ' ⁇ 2 2 .
  • a kernel function is a hyperbolic tangent kernel of the form tanh ⁇ ⁇ x
  • Y > + VS exp 2 ⁇ ⁇ x
  • the main difficulty that arises then, for certain nuclei like the Gaussian nucleus with radial base or the tangent hyperbolic nucleus, is the secure computation of an exponential, appearing in the examples of functions nuclei presented above. Indeed, the calculation of an exponentiation is a complex operation to implement in multiparty secure computing protocols.
  • (( f (x, y ) + r) mod T ) would be randomly distributed uniformly in the space T and therefore no information on f (x, y) could be deduced.
  • the process becomes inaccurate and does not always return the correct result because e f ( x, y ) is not always equal to e ( f (x, y) + r ) mod T / e r .
  • An object of the invention is to provide a method for classifying a data securely with a support vector machine whose evaluation of the core may include an exponentiation.
  • the proposed method makes it possible to calculate in a secure manner between two parts a function that is written as a product of sub-functions of two variables and two functions of a variable (possibly constants).
  • the method makes it possible to simply evaluate such a function by decomposing it into elementary exponential components that depend only on a single bit of the data to be classified.
  • processing units 10, 20 are shown respectively comprising a client unit 10 and a server unit 20.
  • Each processing unit comprises processing means, for example a processor 11, 21 adapted to implement calculations or operations on data, and to execute a program comprising code instructions installed on the processor.
  • Each processing unit also comprises a memory 12, 22, and a communication interface 13, 23 with the other party.
  • the data X is advantageously a data item to classify.
  • Data X can be representative of an object or a physical quantity. It may have been obtained from a sensor or an interface.
  • the data X can be a digital acquisition of a biometric trait of an individual.
  • the classification of the data consists of checking whether the data corresponds to an acquisition made on a living tissue or not, in which case a fraud can be detected.
  • the classification of the data item X is then implemented by means of a support vector machine comprising a classifier H using a kernel function, which may comprise an exponential.
  • the server unit 20 holds the parameters of the classifier H.
  • N is a positive prime number
  • j is a mute index with values from 1 to N
  • ⁇ j , ⁇ j , and Y j are the parameters of the classifier.
  • the server-unit 20 holds the parameters ⁇ j , ⁇ j , and Y j , for j from 1 to N.
  • k j , Y j and C j are the parameters of the classifier.
  • the server unit 20 then holds the parameters k j , Y j and C j , for all j from 1 to N.
  • classifier nuclei exist, for example a homogeneous or inhomogeneous polynomial nucleus.
  • the processing units 10, 20 can engage in a method of classifying the data X held by the client unit 10.
  • the method advantageously comprises a first step 100 of bringing back the data held by the client. unit client 10 to a datum expressed in base q, that is to say whose all components have integer values between 0 and q-1, where q is an integer strictly greater than 1.
  • This step comprises the approximation of the data X by a data X 'whose components X' i are integers, in order then to be able to implement with the quantized data a secure calculation.
  • SMC secure computing
  • the data X ' is a binary data whose components have values in ⁇ 0,1 ⁇ .
  • p is a positive integer
  • i is a mute index with values from 1 to p.
  • the data X is binarized, its quadratic norm is also binarized.
  • step 200 all the calculations are carried out as a whole integers between 0 and m-1, with m a positive integer first.
  • the value of m is adapted according to the function F, so that the space contains all the possible results of the function F.
  • it is also restricted to functions f i and inputs X, Y such that f i (x i , Y) is never zero.
  • the function F is the core function h j of the carrier vector machine or a part thereof, possibly multiplied by a scale factor a as explained above. after, and quantified.
  • the nuclei h j are therefore all calculated for j from 1 to N.
  • the figure 3 illustrates an example of implementation of step 200 for a general case where the server unit holds a data Y, the client unit holds the data X, and the data engage in the calculation of F (X , Y).
  • the server-unit may hold a set of N data (Y 1 , ..., Y N ), and the method may have the objective of calculating the evaluation of the function in the data of the client-unit and each data of the server-unit, that is to say all F (X, Y j ) with j between 1 and N.
  • F X, Y j
  • the method 200 comprises a first step 210 in which the server-unit randomly generates a masking data set r i indexed invertible for propagation throughout .
  • the server-unit In the case where the server-unit holds several data Y j , it randomly generates as many sets of data r i, j that it holds data.
  • the method 200 then comprises a step 220 during which the server-unit generates, from these data r i , and for all i from 1 to n, a set of elements such that each element is a possible result of the function f i evaluated in the data of the client-unit, which is therefore unknown to it, and the data of the server-unit, multiplied by a data r i .
  • the set of elements generated for each i is the doublet: r i ⁇ f i 0 Y , r i ⁇ f i 1 Y .
  • the set of elements is a q-tuple: r i ⁇ f i 0 Y , ... , r i ⁇ f i q - 1 , Y .
  • the server unit can generate only n q-tuple, or a q-tuple per component of the data of the client unit.
  • each element of each q-tuple is the concatenation of the results of the product of an indexed data r i with the evaluation of the sub-function of two variables f i into an element a of the set of integers of 0 to q-1, and in each of the N data Y j of the server unit: r i , 1 ⁇ f i at Y 1 ⁇ ...
  • the method then comprises a step 230 in which the client unit and the server unit engage in an unconscious transfer protocol, and where the client retrieves, for each i from 1 to n, one of the elements generated by the server in step 120 as a function of the value of x i .
  • the implementation of the unconscious transfer protocol depends on the implementation of the previous step 120.
  • the client unit In the first of the two cases described above, the client unit must implement a number n * N of type 1 subconscious transfers among q with inputs of the server unit on m bits to recover intermediate data for all doublets. In the second case, it realizes only n unconscious transfers of type 1 among q, with entries of the server-unit on m.N bits.
  • the unconscious transfers are of type 1 out of 2 in the case where the data of the client unit is binary.
  • This protocol makes it possible to extend ⁇ unconscious transfers on entries of ⁇ bits (where ⁇ is a security parameter often equal to 80 or 128), in n transfers unconscious on I bits, with n> ⁇ and l> ⁇ , using only efficient symmetric cryptographic operations, such as hash functions or pseudo-random functions (or PRFs for pseudo-random function).
  • the client unit therefore has, for each i of 1 to n and for each data Y (j) of the server-unit, an intermediate data equal to evaluating the sub-function f i in its data and the data of the server unit, multiplied by the corresponding data item r i (j) , which is a masking data of the intermediate result f i ( x i , Y ( j ) ) .
  • the method also comprises a step 240 in which the server unit performs, for each data item it holds, the multiplication of the set of all the inverse r i -1 of the data r i corresponding to the data Y, and multiplied by evaluating the sub-function of the second variable in its data f Y (Y).
  • the client unit can communicate to the server-unit its result R.
  • the server-unit then calculates, for each data item Y (j) , the product of T and R (j) which gives the same result F (X, Y).
  • the result F (X, Y) can then be used by one of the parties, advantageously in a cryptographic application 300 (for example signature, encryption, etc.).
  • a cryptographic application 300 for example signature, encryption, etc.
  • each subfunction f i can understand an exponential term.
  • the classifier H thus comprises a sum of functions F j which must all be evaluated in a secure manner.
  • the function quant (x) is an integer quantization function of the element x. For example, it can be the nearest whole round. In order to obtain a more precise result, we can multiply the quantized term by a scale factor a>1; the larger a is, and the lower the information loss at the quant level is small.
  • the subfunctions f ⁇ l + i make it possible to calculate the term ⁇ e - ⁇ ⁇ X ' ⁇ 2 2 .
  • the parameters held by the server-unit are the Y j , ⁇ j and C j , for all j from 1 to N,
  • the step 260 of calculating the result is not implemented so that no part has an intermediate result before the result of the classification of the data item X.
  • This step is implemented using a Boolean circuit to be evaluated by multiparty secure computing between the client unit holding the inputs (T 1 , ... T N ) and the server unit holding the inputs (R 1 , ... R N , b), so that the client unit obtains only the result of the comparison of H (X) to b and the server unit learns no information on X or T j .
  • This step may for example be implemented using the Yao protocol or the Goldreich-Micali-Wigderson protocol (GMW), which are known to the person skilled in the art and recalled in the publication of T. Schneider et al., "GMW vs. Yao? Efficient Secure Two-Partu Computing with Low Depth Circuits ", in Financial Cryptography and Data Security, Volume 7859 of the series Read Notes in Computer Science, pp 275292, 2013 .
  • GMW Goldreich-Micali-Wigderson protocol
  • Yao's protocol was originally introduced in the publication of AC Yao et al., "How to generate and exchange secrets," In Foundations of Computer Science (FOCS'86), pp. 162-167, IEEE 1986 .
  • the GMW protocol was introduced in the publication of O. Goldreich et al., "How to play any mental game", In Symposium on Theory of Computing (STOC'87), pp218-229, ACM (1987) ).
  • the proposed method therefore makes it possible to classify data securely without leakage of information on the intermediate results T j , R j while maintaining good accuracy on the result.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computer Hardware Design (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Computer And Data Communications (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
  • Complex Calculations (AREA)
EP17153545.3A 2016-01-28 2017-01-27 Verfahren zur ausführung einer kryptographischen berechnung und anwendung auf die klassifizierung durch support-vector-maschinen Active EP3200384B1 (de)

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FR1650693A FR3047327B1 (fr) 2016-01-28 2016-01-28 Procede d'execution de calcul cryptographique et application a la classification par machines a vecteurs de support

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CN113194060A (zh) * 2021-03-09 2021-07-30 中国大唐集团科学技术研究院有限公司 一种基于支持向量机算法的电厂工控系统数字量加密传输算法

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US7657028B2 (en) * 2005-10-07 2010-02-02 Mitsubishi Electric Research Laboratories, Inc. Method for classifying private information securely
FR2992124B1 (fr) * 2012-06-18 2014-07-25 Morpho Procede de traitement de donnees securise

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KENG-PEI LIN ET AL: "On the Design and Analysis of the Privacy-Preserving SVM Classifier", IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, IEEE SERVICE CENTER, LOS ALAMITOS, CA, US, vol. 23, no. 11, 1 November 2011 (2011-11-01), pages 1704 - 1717, XP011353560, ISSN: 1041-4347, DOI: 10.1109/TKDE.2010.193 *
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113067694A (zh) * 2021-03-31 2021-07-02 支付宝(杭州)信息技术有限公司 一种通信优化的双方安全比较方法、装置以及设备

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FR3047327A1 (fr) 2017-08-04
US20170222797A1 (en) 2017-08-03
EP3200384B1 (de) 2018-05-09
FR3047327B1 (fr) 2018-07-27
US10348483B2 (en) 2019-07-09

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